Can I prevent a specific bone from moving during Auto-IK posing?
In Bone settings (Pose mode) find IK controls. Don't mind that they are greyed out, they are still working. Lock these axis (click on "lock icon") to fully exclude desired bones from the IK chain.

How to quickly lock many bones?

Select desired bones and lock axis as described earlier, then click on "lock icon" with right mouse button and select Copy to selected, repeat for every axis (X,Y,Z)